Josh,
I don't mean to be callous, but regardless of your format, 35mm, 16mm, or even dv, shooting a feature at your age is a very bad idea unless you have some pretty extensive experience in planning, shooting, directing and most of all, WRITING for a feature. I'm seriously not joking and am speaking from experience.
Making a quality short film, even a five minute one, can be a tremendously daunting task. I definitely encourage you to explore though, and for your current situtation, I'd strongly recommend doing a 16mm (or if you want to take it up a step, super-16) short under 10 minutes. One, it gives you the discipline in a film production that's essential to every beginning film maker. You can get 16mm cameras for as low as 200 on ebay, or even now, eclair nprs with coaxial magazines sell for around 2000. And two, you begin to learn the "language" of film, the flow of control and direction between different members in your "crew". And three, you get the "look" of film, without it totally bankrupting you the way 35mm would (though it is still expensive).
Although it's more financially feasible to shoot with dv, i'd have to suggest against it. It's not so much the format (though since film is an art and aesthetics do count), it's more the mentality that usually comes with film. I often find that people involved in productions using film (even short films) have a completely different mindset (because you have more at stake, perhaps) than with digital where you rest on a safety net of contingency, but that may be just me. Also, film cameras are almost completely manual and mechanical, meaning that there's total control over the image (again, if you know what you're doing). What I'm getting at is to get the process down until it becomes second nature until you feel you can mentally (and financially) tackle down with 35mm.
Good luck.